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Almost-Hermitian ra...
Almost-Hermitian random matrices and bandlimited point processes
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- Ameur, Yacin (författare)
- Lund University,Lunds universitet,Matematik (naturvetenskapliga fakulteten),Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Sciences),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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- Byun, Sung-Soo (författare)
- Korea Institute for Advanced Study
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(creator_code:org_t)
- 2023
- 2023
- Engelska 57 s.
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Ingår i: Analysis and Mathematical Physics. - 1664-2368. ; 13:3
- Relaterad länk:
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- We study the distribution of eigenvalues of almost-Hermitian random matrices associated with the classical Gaussian and Laguerre unitary ensembles. In the almost-Hermitian setting, which was pioneered by Fyodorov, Khoruzhenko and Sommers in the case of GUE, the eigenvalues are not confined to the real axis, but instead have imaginary parts which vary within a narrow “band” about the real line, of height proportional to 1/N, where N denotes the size of the matrices. We study vertical cross-sections of the 1-point density as well as microscopic scaling limits, and we compare with other results which have appeared in the literature in recent years. Our approach uses Ward’s equation and a property which we call “cross-section convergence”, which relates the large-N limit of the cross-sections of the density of eigenvalues with the equilibrium density for the corresponding Hermitian ensemble: the semi-circle law for GUE and the Marchenko–Pastur law for LUE. As an application of our approach, we prove the bulk universality of the almost-circular ensembles.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- Almost-Hermitian GUE/LUE
- Bandlimited Coulomb gas
- Cross-section convergence
- Ward’s equation
- Translation invariance
Publikations- och innehållstyp
- art (ämneskategori)
- ref (ämneskategori)
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